Question

A 79g , 40-cm-long rod hangs vertically on a frictionless, horizontal axle passing through its center. A 15g ball of clay traveling horizontally at 2.0m/s hits and sticks to the very bottom tip of the rod.

To what maximum angle, measured from vertical, does the rod (with the attached ball of clay) rotate?

Answer 1

Answer 2

Apply consrvation of angular momentum

m*v*(L/2) = I*w

m*v*L/2 = (M*L^2/12 + m*(L/2)^2))*w

w = (m*v*L/2)/(M*L^2/12 + m*(L/2)^2))

= (15*2*0.4/2)/(79*0.4^2/12 + 15*0.2^2)

= 3.63 rad/s

now Apply Ebergy consrvation

0.5*I*w^2 = m*g*h

h = 0.5*I*w^2/(m*g)

= 0.5*((M*L^2/12 + m*(L/2)^2))*3.63^2/(m*g)

= 0.5*(79*0.4^2/12 + 15*0.2^2)*3.63^2/(15*9.8)

= 0.0741 m

= 7.41 cm

h = L*(1 - cos(thet))

h/L = 1 - cos(theta)

cos(theta) = 1 - h/L

theta =cos^-1(1 - h/L)

= cos^-1(1 - 7.41/40)

= 35.44 degrees <<<<<<<-------------Answer